Fault reconstruction in linear dynamic systems using multivariate statistics

Treasure et al. (2004) recently proposed a new sub space-monitoring technique, based on the N4SID algorithm, within the multivariate statistical process control framework. This dynamic-monitoring method requires considerably fewer variables to be analysed when compared with dynamic principal component analysis (PCA). The contribution charts and variable reconstruction, traditionally employed for static PCA, are analysed in a dynamic context. The contribution charts and variable reconstruction may be affected by the ratio of the number of retained components to the total number of analysed variables. Particular problems arise if this ratio is large and a new reconstruction chart is introduced to overcome these. The utility of such a dynamic contribution chart and variable reconstruction is shown in a simulation and by application to industrial data from a distillation unit.

Improved reliability in diagnosing faults using multivariate statistics

This paper analyses multivariate statistical techniques for identifying and isolating abnormal process behaviour. These techniques include contribution charts and variable reconstructions that relate to the application of principal component analysis (PCA). The analysis reveals firstly that contribution charts produce variable contributions which are linearly dependent and may lead to an incorrect diagnosis, if the number of principal components retained is close to the number of recorded process variables. The analysis secondly yields that variable reconstruction affects the geometry of the PCA decomposition. The paper further introduces an improved variable reconstruction method for identifying multiple sensor and process faults and for isolating their influence upon the recorded process variables. It is shown that this can accommodate the effect of reconstruction, i.e. changes in the covariance matrix of the sensor readings and correctly re-defining the PCA-based monitoring statistics and their confidence limits. (c) 2006 Elsevier Ltd. All rights reserved.

The role of previous experience and attitudes toward statistics in statistics assessment outcomes among undergraduate psychology students

Previous research has demonstrated that students’ cognitions about statistics are related to their performance in statistics assessments. The purpose of this research is to examine the nature of the relationships between undergraduate psychology students’ previous experiences of maths, statistics and computing; their attitudes toward statistics; and assessment on a statistics course. Of the variables examined, the strongest predictor of assessment outcome was students’ attitude about their intellectual knowledge and skills in relation to statistics at the end of the statistics curriculum. This attitude was related to students’ perceptions of their maths ability at the beginning of the statistics curriculum. Interventions could be designed to change such attitudes with the aim of improving students’ learning of statistics.

The effect of statistics anxiety on students’ predicted and actual test scores

This study investigated the effect of statistics anxiety and attitudes on first year psychology students’ predicted and actual statistics class test scores. A total of 52 students completed the Statistics Anxiety Rating Scale and estimated their class test scores one week before their test at the end of first year. Regression models were conducted with the six attitude and anxiety subscales as predictors and the predicted and actual test scores as criterion variables. The results showed that computation self concept and fear of asking for help accounted for 37% of the variance in predicted test scores. However, when actual test scores were analysed the significant predictors were worth of statistics and interpretation anxiety, which accounted for 20% of the variance. These results suggested that while statistics anxiety does influence students’ perceptions of their competence it appears to have less effect on their actual performance. Results also suggested that students were unaware of their own statistical competence. Remedial action is required to address the level of statistics anxiety experienced by first year undergraduate psychology students, as it appears to result in unrealistic assessments of their ability and has detrimental effects on their statistics self-efficacy.